Development of piezo-driven compliant bridge mechanisms: general analytical equations and optimization of displacement amplification

Compliant bridge mechanisms are frequently utilized to scale micrometer order motions of piezoelectric actuators to levels suitable for desired applications. Analytical equations have previously been specifically developed for two configurations of bridge mechanisms: parallel and rhombic type. Based on elastic beam theory, a kinematic analysis of compliant bridge mechanisms in general configurations is presented. General equations of input displacement, output displacement, displacement amplification, input stiffness, output stiffness and stress are presented. Using the established equations, a piezo-driven compliant bridge mechanism has been optimized to maximize displacement amplification. The presented equations were verified using both computational finite element analysis and through experimentation. Finally, comparison with previous studies further validates the versatility and accuracy of the proposed models. The formulations of the new analytical method are simplified and efficient, which help to achieve sufficient estimation and optimization of compliant bridge mechanisms for nano-positioning systems.